[t_mann]

That way you should be able design a disc-shaped earth with constant strength of the gravitational force on the whole surface. But it would still have a center of mass (likely lying outside the shape you're describing, in the void beneath the center point), and the direction of the force should still be pointing towards that center, no? So the problem the GP has described, that you're starting to tilt as you move towards the edge, should remain in principle.

[benterris]

I believe the strength of gravitational force would not be constant either, as your center of mass would still have a fixed location, so every point on the disc have different distances to that center of mass (in addition to not being orthogonal to the surface). But maybe it might be approximated with an infinitely long cylinder, so the center of mass is infinitely far away below the surface ?

[t_mann]

The thinking in the other post, that the mass increases as you move away from the center, in a manner that the two effects cancel out, intuitively seems like it should be feasible. Remember that the center of mass is just an abstraction, you need to take the full integral over all mass to get the force vector at each point. And if you're closer to more mass further away from the center, which a shape like the one described above should give you, it might work. But one would have to do the math to be sure.

Edit: come to think of it, maybe that effect would let you adjust the direction of the force, too. Thinking about center of mass can be treacherous with more complex shapes...